A study of a stochastic model for stock prices

The goal of this thesis is to present, explain, and analyze a stochastic model of stock behavior.

The main body of this text is inspired by A.G. Malliaris' article entitled "Itô's Calculus in Financial Decision Making," published in volume 25, number 4, of the SIAM REVIEW in October, 1983.

Stochastic processes, Wiener processes, Itô's stochastic differential equation, and Itô's formula are the main mathematical concepts of this paper. This thesis will clearly present these concepts and their relation to modeling the price of a stock. An intuitive understanding of this stock model is gained through graphical analysis of computer simulations.

This stochastic model of stock behavior, though simplistic, is a commonly used one in finance theory. It is capable of predicting the probabilities of certain gains or losses in the value of the stock at any time t. This model is also used in the derivation of the Black-Scholes formula, as well as other option pricing strategies.